Molecule Types | <Prev Next> |
See Making a linear molecule data file and the worked example: The Schumann-Runge Bands of O2 for an introduction to working with linear molecules.
PGOPHER will calculate Hund's cases (a) and (b) exactly, and will work with the other possible cases, though these typically require more work to set up.
J |
Total angular momentum
excluding
nuclear spin |
F |
Total angular momentum |
S |
Total electron spin angular momentum. This must be set for each State |
N |
J-S = Total angular momentum excluding nuclear and electron spin. |
Λ | The projection of the electronic orbital angular momentum onto the z axis of the molecule. This must be set for each State |
Ω | The projection of J onto the axis of the
molecule; Ω
= Λ + Σ where Σ is the projection of S
onto the axis of the molecule. |
Fn |
The notation F1, F2,
F3 ... is an alternative notation for the
components of a multiplet, ordered by energy with with F1
being the lowest. |
|Name J +- Omega>where Name is the manifold and state name. If hyperfine structure is included in the calculation then F (and intermediate quantum numbers if there is more than one nucleus) is added to the end.
Name |
The manifold and state name |
J |
The J quantum number; not shown if ShowJ is false at the Molecule level |
N |
The N quantum number; not shown if ShowN is false at the Molecule level or all states are singlet states |
Ω | The Ω quantum number; not shown if ShowOmega is false at the Molecule level (the default) or all states are singlet states |
Fn |
The component of the
multiplet
numbered from 1 in order of increasing energy; not shown if
ShowFNumber is
false at the Molecule
level or all states are singlet
states. This contains the same information as the Ω quantum
number, so
it does not usually make sense to show both. |
e/f |
The parity; not shown if Showef is false at the Molecule level. |
Hyperfine quantum numbers are
added at the end as required. |
X v=0 7.5 7 F1e
Note that the only guaranteed quantum numbers are the total
angular momentum and symmetry; while PGOPHER tries to work out
sensible assignments of the other quantum numbers there are
cases where
this is not possible, or the choice the program makes is not the
same
as other programs. This most commonly arises in the case of
perturbations, or where S
> J.
The algorithm used can be adjusted by the EigenSearch and LimitSearch settings
at the Manifold level; you may want
to use LimitSearch = True
as this can
give more consistent results for the F1/F2...
and
N labels. Variations in the
quantum number assignment does not affect other parts of the
calculation, so the simulated positions and intensities are not
affected by these considerations.
The general format is ΔNΔJFn'Fn"p"(J)
though, as for the state labels
above some elements may be omitted:
ΔN | The change in the N quantum number expressed as a P, Q or R; not shown if ShowN is false at the Molecule level or all states are singlet states |
ΔJ | The change J quantum number, expressed as P, Q or R. |
Fn'Fn" | The upper and lower
(spin-orbit)
component number. If the two numbers are the same, only
one number is
shown. |
p" | The lower state parity,
expressed as e
or f. |
F',F |
If nuclear spin is included, the upper and lower state hyperfine (F) quantum numbers are added. |
For example, a 2Π - 2Π band may give
the
following transition:
rR1e(6.5) A v=0 7.5 7 F1e - X v=0 6.5 6 F1e
implying ΔN = +1 ( r ),
ΔJ = +1 ( R ),
F1
- F1 (1), e-e, J"
= 6.5.